1 to 5 NUMBER Numbers and Operations Place Value, Rounding and Estimation Understanding Products ALGEBRA Expressions and Formulae

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1 Numbers and Operations Four operations and numbers Inverse operations Fractions as Operators Fractions and Terminating decimals Place Value, Rounding and Estimation Ordering decimals Rounding Estimation Using inequality notation Understanding Products Factors and Multiples Primes and Prime Factorisation Powers and Roots Indices Standard Form 1 to 5 NUMBER ALGEBRA Expressions and Formulae Algebraic Notation Simplifying expressions Substitution Expanding Factorising Understanding expressions as functions Equations, Inequalities and Identities Understand the difference between equations and identities Solve any linear equation Solve linear inequalities and represent on a number line Solve quadratic by factorising Linear Graphs Draw straight line graphs Find gradients of straight lines Use gradient and intercepts Find equations of parallel lines Solve linear simultaneous equations Non- Linear Graphs Draw any graph given its equation Recognise a graph Find roots, intercepts and turning points of quadratics Sequences Use term- to- term and position to term rules Recognise square, cube, triangular, Fibonacci type, quadratic and geometric sequences Find and use nth terms of linear sequences.

2 PROPORTION AND RATES OF CHANGE Understanding Proportion Understand proportional relationships as based on multiplying Write proportions as fractions Solve proportion problems (inc best buy etc) Write and use ratio Write ratios and functions Understand inverse proportion Percentages Understand percentages as how many in 100 parts Calculate percentages Write proportions and changes as percentages Calculate percentage changes Use percentages over 100% Units, Scales and Proportions Convert units Use compound units Understand scale pictures as being in proportion Use maps and scale diagrams GEOMETRY AND MENSURATION Measures Measure lines Measure angles Estimate and use different units of measurement Use compass directions and bearings Accurate and Inaccurate Diagrams Symmetries Basic Angle properties Scale Drawing and Bearings Constructions and Loci Similarity and Congruence Triangles Angles in Triangles Triangle Congruence Area of a Triangle Pythagoras Basic Trigonometry Polygons

3 Properties of quadrilaterals Area of quadrilaterals Angles in quadrilaterals Angle properties of polygons Polyhedra Faces, Edges, Vertices Plans and Elevations Surface Area and Volume of Cuboids, Prisms and Pyramids Curved Shapes Circle Nomenclature Circle Circumference and Area Arc Length and Sector Area Surface Area and Volume of Cylinders, Cones and Spheres Working with multiples of π Transformations and Vectors Reflections Rotations Enlargements (inc fractional s.f.) Translations Basic vectors PROBABILITY AND STATISTICS Probability of a single event Write probabilities Predict number of outcomes of an event Mutually exclusive events Exhaustive lists Relative Frequency vs Theoretical probability Probability of two or more events Systematic listing Possibility spaces, Venn Diagrams, Tree Diagrams Find probability of independent and dependent events Sampling and data collection Understand the usefulness and limitations of sampling Judge bias in a sample Write questionnaires Categorical data Understand data types Represent categorical data using frequency tables, pictograms, bar charts, and pie charts. Choose and compare categorical data from their diagrams. Numerical data Draw vertical line graphs to represent ungrouped numerical data Draw tables and line graphs for time series data Calculate mode, median, mean and range Compare using an average and range Grouping discrete and continuous data Find averages from tables Draw and analyse scatter graphs, and understand their use.

4 PROBLEM SOLVING Financial Calculations Calculate with bills Work with debits and credits Calculate wages Calculate income tax, VAT etc Forming equations Equations from shapes (perimeters, angles etc) Equations from other situations Graphical Problem Solving Use graphs of speed, distance, time, velocity etc Find and interpret the gradient of distance- time graphs and the area under velocity- time graphs Find and interpret the gradient of other piecewise linear graphs. Estimates and the Limits of accuracy Use estimates in practical situations Judge appropriate accuracy Number problems Set up and solve growth and decay problems (compound percentages) Compare proportions as percentage, fraction and decimal Direct and inverse proportion problems Percentage problems

5 5 to 9 NUMBER Rounding, Estimation and the Limits of Accuracy Round to a given accuracy in significant figures Round to a suitable accuracy Estimate roots Use inequalities notations to show the results of rounding Find and calculate with upper and lower bounds Understanding Products Prime Factorisation and index form Powers and Roots Indices Standard Form Factorials and Multiplicative counting Rational and Irrational numbers Convert between fractions and recurring decimals Calculate with Fractions Simplify and perform basic calculations with Surds Work with multiples of π ALGEBRA Expressions, Formulae and Functions Expand products of binomials Factorise linear and quadratic expressions Understand an expression as a function and its links to formulae Find the inverse function (using correct notation) and link to rearranging a formula Find and evaluate a composite function (using correct notation) Complete the square for a quadratic expression Prove algebraic results Equations, Inequalities and Identities Understand the difference between equations, inequalities and identities Solve any linear equation (including those with fractions, unknowns on both sides etc) Solve quadratics by factorising, using the formula and completing the square Solve linear and non- linear simultaneous equations Solve, represent and interpret inequalities in one or two variables, including simple quadratic inequalities Linear Graphs Use gradient and intercepts Find equations of parallel and perpendicular lines Solve linear simultaneous equations Non- Linear Graphs Draw any graph given its equation Recognise a graph Find roots, intercepts and turning points of quadratics Graphically solve non- linear simultaneous equations. Draw and interpret circle equations Sequences Recognise square, cube, triangular, Fibonacci type, quadratic and geometric sequences

6 Use position to term rules of any sequence (including geometric sequences with irrational values of r) Find and use nth terms of linear and quadratic sequences Iterative methods Apply iterative methods to provide approximate solutions to equations or solve other problems. PROPORTION AND RATES OF CHANGE Understanding Proportion Understand proportional relationships as based on multiplying Use compound units Write proportions as fractions Write and use ratios and functions Understand inverse proportion Percentages Write proportions and changes as percentages Calculate percentage changes Use percentages over 100% Reverse a percentage change Solve growth and decay problems with percentages Proportion and Graphs Understand the shape of a graph of two quantities that are in direct or inverse proportion. Find the gradient of a straight line graph and interpret that as a rate of change Understand the gradient of a curve as the instantaneous rate of change Work with average and instantaneous rates of change and the links to chords and tangents of graphs Algebraic Proportion Set up algebraic proportional relationships Find constants of proportionality Solve problems involving quantities that are in direct or inverse proportions. GEOMETRY AND MENSURATION Mensuration Area, Surface Area and Volume of shapes Length, Area and Volumes of similar shapes Accurate and Inaccurate Diagrams Loci Bearings Proving Congruence Circle Theorems Transformations and Vectors Reflections Rotations Enlargements (inc fractional/negative s.f.) Translations Understand the changes and invariance under the four transformations. Vectors Pythagoras and Trigonometry in Right Triangles Use Pythagoras Theorem in 2D and 3D Understand and use trigonometric ratios in right- triangles

7 Solve problems involving lengths and angles in right triangles (inc right- angled triangles that can be formed from isosceles and equilateral triangles) Know the exact trig ratios for 0, 30, 45, 60, 90 degrees Trigonometry in non- right triangles Use Sine rule to find lengths and angles in non- right triangles Use Cosine rule to find lengths and angles in non- right triangles Use Sine rule and Cosine rule to find lengths and angles in non- right triangles Find area of any triangle. PROBABILITY AND STATISTICS Probability Possibility spaces, Venn Diagrams, Tree Diagrams Find probability of independent and dependent events Numerical data Create a suitable sample from a given population Draw and analyse scatter graphs, and understand their use Group discrete and continuous data Find averages from tables Draw and analyse cumulative frequency diagrams and link box plots Draw histograms for data with unequal class widths. Carry out analysis of histograms.

8 PROBLEM SOLVING Number problems Upper and lower bounds with measures and formulae (with values given in standard form) Using factorials and multiplication for counting for practical situations Graphical Problem Solving Use graphs of speed, distance, time, velocity etc Find and interpret the gradient of distance- time graphs and the area under velocity- time graphs Find and interpret the gradient of other piecewise linear graphs Solve problems with exponential graphs Iterative Processes Solve practical problems requiring iterative processes Coordinate Geometry Apply circle theorems, Pythagoras and trigonometry to shapes defined on a Cartesian axes Transform any graph Algebraic problems Add, Subtract, Multiply, Divide and Simplify fractions defined using Algebra Set up and solve problems involving simultaneous equations Set up and solve simple linear programming problems